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They differ from each other on the focused image levels, and thus have disparate performance. The former tackles the filling-in problem by diffusing the image from the known surrounding regions into the missing region at the pixel level by using the variational principles and partial differential equations (PDE). Hence, it is superior for structure propagation or relatively smaller missing region, yet poor in handling textured or large region due to the introduction of smoothing effect. The latter propagates the image information at the patch level based on the texture synthesis technique. By incorporating the patch priorities to determine the filling order, the exemplar-based method can deal with structure propagation as well as texture propagation, and hence outperforms the diffusion-based one with respect to large missing region.
Key Terms in this Chapter
Inpainting: Rooted in the restoration of images. Traditionally, inpainting has been done by professional restorers. For instance, in the museum world, in the case of a valuable painting, this task would be carried out by a skilled art conservator or art restorer. In photography and cinema, is used for film restoration; to reverse the deterioration (e.g., cracks in photographs or scratches and dust spots in film; see infrared cleaning). It is also used for removing red-eye, the stamped date from photographs and removing objects to creative effect. In the digital world, inpainting refers to the application of sophisticated algorithms to replace lost or corrupted parts of the image data (mainly small regions or to remove little defects).
Weighted Non-Negative Matrix Factorization (WNMF): A group of structured NMF that enforces other characteristics or structures in the solution to NMF learning problem. WNMF attaches different weights to different elements regarding their relative importance. Weighed formulations are commonly modified versions of learning algorithms, which can be utilized to emphasize the relative importance of different components.
Partial Differential Equations (PDE): The differential equations that contain unknown multivariable functions and their partial derivatives. This is in contrast to ordinary differential equations, which deal with functions of a single variable and its derivatives. They are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.
Sparse Coding: A class of unsupervised methods for learning sets of over-completed bases to represent data efficiently. Given a potentially large set of input patterns, sparse coding algorithms attempt to automatically find a small number of representative patterns which, when combined in the right proportions, reproduce the original input patterns. The sparse coding for the input then consists of those representative patterns.
Singular Value Decomposition (SVD): A factorization of a real or complex matrix in linear algebra. It was originally developed by differential geometers, who wished to determine whether a real bilinear form could be made equal to another by independent orthogonal transformations of the two spaces it acts on. It is closely related to the eigen-decomposition, and has found many applications recently in image engineering (IE).
Image Engineering (IE): An integrated discipline/subject comprising the study of all the different branches of image and video techniques. As a general term for all image techniques, it could be considered as a broad subject encompassing mathematics, physics, biology, physiology, psychology, electrical engineering, computer science, automation, etc. Its advances are also closely related to the development of telecommunications, biomedical engineering, remote sensing, document processing, industrial applications, etc.
Matching Pursuit: A type of numerical technique which involves finding the “best matching” projections of multidimensional data onto an over-complete dictionary.
Non-Negative Matrix Factorization (NMF): A recently developed, biologically inspired method for nonlinearly finding purely additive, sparse, linear, and low-dimension representations of non-negative multivariate data to consequently make latent structure, feature or pattern in the data clear. NMF makes all representation components non-negative (only purely additive representations are allowable) and nonlinearly implements dimension reduction. Psychological and physiological evidence for NMF is that perception of the whole is based on perception of its parts, which is compatible with the intuitive notion of combining parts to form a whole, therefore it is considered to grasp the essence of intelligent or biological data representation in some degree.